All I Ever Wanted to Know About Circles


 Elijah Dawson
 1 years ago
 Views:
Transcription
1 Parts of the Circle: All I Ever Wanted to Know About Circles Important Circle Vocabulary: CIRCLE the set off all points that are the distance from a given point called the CENTER the given from which all points on a are the same RADIUS the distance from the of a circle to any point on the circle DIAMETER the across a circle through its CIRCUMFERENCE the around a AREA the amount of space contained of the circle
2 Calculating Circumference: c = 2 r Example 1: Pi Calculate the circumference of the given circle. 7.2 cm Circumference of a circle: c = 2 r Q: What is Pi? A: Pi is a symbol representing a number that has been calculated out to over 1 million decimal places without stopping or repeating ( )!! To save space, we just use the Greek symbol (sounds like pie spelled like pi). Replace r with 7.2: Use a calculator: Example 2: Calculate the circumference of the given circle. 9 cm If d = 9, r must equal? Circumference of a circle: c = 2 r Replace r with 4.5: Use a calculator:
3 Practice Problems (circumference): Find the circumference of each circle. Round your answer to the nearest tenth and include units in 24 mm 38 mi km 19.4 m 7.25 ft Solve (include units). If needed, round to the nearest hundredth. 7. If the tire on a car has a diameter of 25 inches, how far will the car travel each time the tire completes one rotation? 8. A hiker wants to walk around a circular lake. If the distance from one side to the other is 200 yards, how long will the hike be? 9. A tree has a diameter of 3 feet. How big around is the tree? 10.A tetherball is tied to a pole with a 1.5 meter rope. How far will the ball travel if it swings completely around the pole?
4 Calculating Area of a Circle: A = r 2 Example 1: Calculate the area of the given circle. 2.7 cm Area of a circle: A = r 2 Replace r with 2.7: Solve: Approximate with a calculator: Example 2: Calculate the area of the given circle. 5 in If d = 5, r must equal? Area of a circle: A = r 2 Replace r with 2.5: Solve: Approximate with a calculator:
5 Practice Problems (area): Find the area of each circle. Round your answer to the nearest tenth and include units in 24 mm 38 mi km 19.4 m 7.25 ft Solve (include units). If needed, round your answer to the nearest hundredth. 9. What is the area, in square inches, of a medium 14 inch pizza from the Green Hills deli? 10.Two friends want to fish a circular lake. If the distance from the center of the lake to shore is 300 yards, how large is the lake? 9. A worker needs to carpet a circular room. If the distance across the room is 15 feet, how much carpet will be needed? 10.A California ground squirrel usually stays within 150 yards of its burrow. Find the area of the ground squirrel's world.
6 What if I Already Know the AREA or CIRCUMFERENCE??? STEP 1: decide whether you need the area or circumference formula and write it down STEP 2: substitute the known values from the problem into the formula STEP 3: solve (hint... just like one & two step equations!!) Example 1: Find the radius of the given circle. A = 16 Area of a circle: A = r 2 Replace A with 16 : Solve: Example 2: Calculate the diameter of the given circle. c = 44 ft Circumference of a circle: c = 2 r Replace c with 44: Solve:
7 Practice Problems (known circumference or area): 1. Find the radius of a circle whose area is Find the diameter of a circle whose circumference is 40 feet. Round your answer to the nearest hundredth. 3. Find the radius of a circle whose circumference is 68 inches. Round your answer to the nearest tenth. 4. Find the radius of a circle whose area is If the circumference of a circle is 628 cm, what is the diameter of that circle?
8 6. If the circumference of a circle is 400 cm, what is the radius of that circle? 7. The circumference of the circle below is centimeters, what is the best estimate for the length of the radius? 8. A circle has a circumference that measures 18 inches. What is the radius, in inches of the circle? 9. Find the length of the radius of each circle given the following areas. a. 400 b. 625 c. 16
9 Who Discovered, anyway?... Group Members Directions: You will need one ruler, one piece of string, and the circular objects, which I will be giving you. First: Record which item you are using Second: Wrap the string around the outside of the object and hold the string up to the ruler to measure the circumference. Record the circumference in the table. Third: Stretch the string from one side of the object to the other to measure its diameter. Hold the string up to the ruler, and record the diameter in the table. Fourth: Move on to your next object! Data Collection Item Measured Circumference Diameter C d The more accurate you measure your circumference and diameter, the closer c d will resemble, the number we call!!!
SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid
Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.
More informationBasic Math for the Small Public Water Systems Operator
Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationUnit 1  Radian and Degree Measure Classwork
Unit 1  Radian and Degree Measure Classwork Definitions to know: Trigonometry triangle measurement Initial side, terminal side  starting and ending Position of the ray Standard position origin if the
More informationMeasurement/Volume and Surface Area LongTerm Memory Review Grade 7, Standard 3.0 Review 1
Review 1 1. Explain how to convert from a larger unit of measurement to a smaller unit of measurement. Include what operation(s) would be used to make the conversion. 2. What basic metric unit would be
More informationALGEBRA I (Common Core)
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, August 12, 2015 8:30 to 11:30 a.m. MODEL RESPONSE SET Table of Contents Question 25...................
More informationMultistep Word Problems
Solutions are at the end of this file. Use after Delta Lesson 15 Multistep Word Problems The Student Text includes some fairly simple two step word problems. Some students may be ready for more challenging
More informationGeometry: Measuring Area and Volume
C H A P T E R Geometry: Measuring Area and Volume 3 33 Aaron Haupt How is math used in packaging candy? When marketing a product such as candy, how the product is packaged can be as important as how it
More informationKeystone National High School Placement Exam Math Level 1. Find the seventh term in the following sequence: 2, 6, 18, 54
1. Find the seventh term in the following sequence: 2, 6, 18, 54 2. Write a numerical expression for the verbal phrase. sixteen minus twelve divided by six Answer: b) 1458 Answer: d) 16 12 6 3. Evaluate
More informationSurface Area and Volume Cylinders, Cones, and Spheres
Surface Area and Volume Cylinders, Cones, and Spheres Michael Fauteux Rosamaria Zapata CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable
More information121 Representations of ThreeDimensional Figures
Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 121 Representations of ThreeDimensional Figures Use isometric dot paper to sketch each prism. 1. triangular
More information12 Surface Area and Volume
12 Surface Area and Volume 12.1 ThreeDimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids
More informationPreAlgebra Exam Review Review for Part 2: You may use a calculator to solve these problems.
PreAlgebra Exam Review Review for Part 2: You may use a calculator to solve these problems. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More information4 th Grade Summer Mathematics Review #1. Name: 1. How many sides does each polygon have? 2. What is the rule for this function machine?
. How many sides does each polygon have? th Grade Summer Mathematics Review #. What is the rule for this function machine? A. Pentagon B. Nonagon C. Octagon D. Quadrilateral. List all of the factors of
More informationEVERY DAY COUNTS CALENDAR MATH 2005 correlated to
EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 35 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:
More informationChapter 1 Problems. 1micron 1 10 6 m =1 10 9 microns. =1 10 4 cm. 1micron 1 10 6 m = 9.144 105 microns. 1 ft
Chapter 1 Problems 1.3 The micrometer is often called the micron. (a) How man microns make up 1 km? (b) What fraction of a centimeter equals 1µm? (c) How many microns are in 1.0 yard We begin by calculating
More informationIllinois State Standards Alignments Grades Three through Eleven
Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other
More informationTask: Representing the National Debt 7 th grade
Tennessee Department of Education Task: Representing the National Debt 7 th grade Rachel s economics class has been studying the national debt. The day her class discussed it, the national debt was $16,743,576,637,802.93.
More informationTrigonometry LESSON ONE  Degrees and Radians Lesson Notes
210 180 = 7 6 Trigonometry Example 1 Define each term or phrase and draw a sample angle. Angle Definitions a) angle in standard position: Draw a standard position angle,. b) positive and negative angles:
More informationTenths, Hundredths, and Thousandths
Mastery Drill Tenths, Hundredths, and Thousandths You remember that and can be written as common fractions or as decimal fractions. = 0. 0 = 0.0 two two Mixed numbers in or can also be written both ways.
More information1) (3) + (6) = 2) (2) + (5) = 3) (7) + (1) = 4) (3)  (6) = 5) (+2)  (+5) = 6) (7)  (4) = 7) (5)(4) = 8) (3)(6) = 9) (1)(2) =
Extra Practice for Lesson Add or subtract. ) (3) + (6) = 2) (2) + (5) = 3) (7) + () = 4) (3)  (6) = 5) (+2)  (+5) = 6) (7)  (4) = Multiply. 7) (5)(4) = 8) (3)(6) = 9) ()(2) = Division is
More informationChapter 4: The Concept of Area
Chapter 4: The Concept of Area Defining Area The area of a shape or object can be defined in everyday words as the amount of stuff needed to cover the shape. Common uses of the concept of area are finding
More informationPAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE
PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE 1 Property of Paychex, Inc. Basic Business Math Table of Contents Overview...3 Objectives...3 Calculator...4 Basic Calculations...6 Order of Operation...9
More information7.2 Quadratic Equations
476 CHAPTER 7 Graphs, Equations, and Inequalities 7. Quadratic Equations Now Work the Are You Prepared? problems on page 48. OBJECTIVES 1 Solve Quadratic Equations by Factoring (p. 476) Solve Quadratic
More informationGeorgia Online Formative Assessment Resource (GOFAR) AG geometry domain
AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent
More informationGrade 4  Module 5: Fraction Equivalence, Ordering, and Operations
Grade 4  Module 5: Fraction Equivalence, Ordering, and Operations Benchmark (standard or reference point by which something is measured) Common denominator (when two or more fractions have the same denominator)
More informationSection 2.4 Law of Sines and Cosines
Section.4 Law of Sines and osines Oblique Triangle A triangle that is not a right triangle, either acute or obtuse. The measures of the three sides and the three angles of a triangle can be found if at
More informationFree PreAlgebra Lesson 55! page 1
Free PreAlgebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can
More information$566.30. What is the monthly interest rate on the account? (Round to the nearest hundredth of a percent.) 4 = x 12. 7)
Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1)What percent of 6 is 27? 1) 2)64.288 is 28.7% of what number? 2) 3)112% of what number is
More informationSolar System Math Comparing Size and Distance
National Aeronautics and Space Administration NASA Explorer Schools PreAlgebra Unit Lesson 1 Student Workbook ANSWER GUIDE Solar System Math Comparing Size and Distance What are the parts of the solar
More information72 Solving Exponential Equations and Inequalities. Solve each equation. 1. 3 5x = 27 2x 4 SOLUTION:
72 Solving Exponential Equations and Inequalities Solve each equation. 1. 3 5x = 27 2x 4 3. 2 6x = 32 x 2 12 2. 16 2y 3 = 4 y + 1 10 4. 49 x + 5 = 7 8x 6 3. 2 6x = 32 x 2 5. SCIENCE Mitosis is a process
More informationArea & Volume. 1. Surface Area to Volume Ratio
1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.
More informationHow many golf balls would it take to circle the Earth at the equator?*
COPYRIGHT NOTICE: Lawrence Weinstein & John A. Adam: Guesstimation is published by Princeton University Press and copyrighted, 2008 by Princeton University Press. All rights reserved. No part of this book
More informationMath. So we would say that the volume of this cube is: cubic units.
Math Volume and Surface Area Two numbers that are useful when we are dealing with 3 dimensional objects are the amount that the object can hold and the amount of material it would take to cover it. For
More informationSolutions to Exercises, Section 5.1
Instructor s Solutions Manual, Section 5.1 Exercise 1 Solutions to Exercises, Section 5.1 1. Find all numbers t such that ( 1 3,t) is a point on the unit circle. For ( 1 3,t)to be a point on the unit circle
More informationSection 6.1 Angle Measure
Section 6.1 Angle Measure An angle AOB consists of two rays R 1 and R 2 with a common vertex O (see the Figures below. We often interpret an angle as a rotation of the ray R 1 onto R 2. In this case, R
More informationAdvanced GMAT Math Questions
Advanced GMAT Math Questions Version Quantitative Fractions and Ratios 1. The current ratio of boys to girls at a certain school is to 5. If 1 additional boys were added to the school, the new ratio of
More informationExam 1 Review Questions PHY 2425  Exam 1
Exam 1 Review Questions PHY 2425  Exam 1 Exam 1H Rev Ques.doc  1  Section: 1 7 Topic: General Properties of Vectors Type: Conceptual 1 Given vector A, the vector 3 A A) has a magnitude 3 times that
More informationYOU CAN COUNT ON NUMBER LINES
Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and
More informationActivity One: Activate Prior Knowledge: Powers of Ten Video and Explore the sizes of various objects in the solar system
Scale in the Solar System  SIXTH GRADE SCIENCE STANDARDS: STANDARD FOUR Students will understand
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationNASA Explorer Schools PreAlgebra Unit Lesson 2 Student Workbook. Solar System Math. Comparing Mass, Gravity, Composition, & Density
National Aeronautics and Space Administration NASA Explorer Schools PreAlgebra Unit Lesson 2 Student Workbook Solar System Math Comparing Mass, Gravity, Composition, & Density What interval of values
More informationALGEBRA I (Common Core)
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m. MODEL RESPONSE SET Table of Contents Question 25..................
More information11.3 Sectors and Arcs Quiz
Name: lass: ate: I:.3 Sectors and rcs Quiz Multiple hoice Identify the choice that best completes the statement or answers the question.. ( point) Jenny s birthday cake is circular and has a 30 cm radius.
More informationWheeled Vehicle Design For Science Olympiad By Carey I. Fisher
Wheeled Vehicle Design For Science Olympiad By Carey I. Fisher The Wheeled Vehicle competition requires that the vehicle travel a specific distance set by the judge at the time of the contest. So the problem
More informationManitoba Curriculum. Alignment with Mathletics. Supported by independent evidencebased research and practice. Powerful reporting.
Supported by independent evidencebased research practice. Follows provincial curricula Powerful reporting Student centred Content Kindergarten Grade 1 Grade 2 02 04 08 Grade 10 Applied & PreCalculus
More informationFSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers
FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward
More informationUnderstanding image scale and resolution
Understanding image scale and resolution Ned Horning Version: 1.0 Creation Date: 20040101 Revision Date: 20040101 License: This document is licensed under a Creative Commons AttributionShare Alike
More information10 7, 8. 2. 6x + 30x + 36 SOLUTION: 89 Perfect Squares. The first term is not a perfect square. So, 6x + 30x + 36 is not a perfect square trinomial.
Squares Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it. 1.5x + 60x + 36 SOLUTION: The first term is a perfect square. 5x = (5x) The last term is a perfect
More informationNEW MEXICO Grade 6 MATHEMATICS STANDARDS
PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical
More information85 Angles of Elevation and Depression. The length of the base of the ramp is about 27.5 ft.
1.BIKING Lenora wants to build the bike ramp shown. Find the length of the base of the ramp. The length of the base of the ramp is about 27.5 ft. ANSWER: 27.5 ft 2.BASEBALL A fan is seated in the upper
More informationThe following table lists metric prefixes that come up frequently in physics. Learning these prefixes will help you in the various exercises.
Chapter 0 Solutions Circles Learning Goal: To calculate the circumference or area of a circle Every day, we see circles in compact disks, coins, and wheels, just to name a few examples Circles are also
More informationXV. Mathematics, Grade 10
XV. Mathematics, Grade 10 Grade 10 Mathematics Test The spring 2011 grade 10 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework
More information(15.) To find the distance from point A to point B across. a river, a base line AC is extablished. AC is 495 meters
(15.) To find the distance from point A to point B across a river, a base line AC is extablished. AC is 495 meters long. Angles
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationAP Physics 1 and 2 Lab Investigations
AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks
More informationPractice Tests Answer Keys
Practice Tests Answer Keys COURSE OUTLINE: Module # Name Practice Test included Module 1: Basic Math Refresher Module 2: Fractions, Decimals and Percents Module 3: Measurement Conversions Module 4: Linear,
More informationBASIC MATH FORMULAS  CLASS I. A. Rectangle [clarifiers, ponds] I = length; w = width; A = area; area in square ft [sq ft]
WASTEWATER MATH CONVERSION FACTORS 1. 1 acre =43,560 sq ft 2. 1 acre =2.47 hectares 3. 1 cu ft [of water] = 7.48 gallons 4. 1 cu ft [of water] = 62.4 Ibs/ft 3 5. Diameter =radius plus radius, D =r + r
More informationExperiment #1, Analyze Data using Excel, Calculator and Graphs.
Physics 182  Fall 2014  Experiment #1 1 Experiment #1, Analyze Data using Excel, Calculator and Graphs. 1 Purpose (5 Points, Including Title. Points apply to your lab report.) Before we start measuring
More informationVirginia Placement Test Practice Questions and Answers
Virginia Placement Test Practice Questions and Answers Table of Contents Practice Problems for UNIT 1 Operations with Positive Fractions... 1 Practice Problems for UNIT Operations with Positive Decimals
More informationDiametral Pitch Gear Ratios Herringbone Gears Idler Gear Involute Module Pitch Pitch Diameter Pitch Point. GEARSIDS Optional Gear Set Straight Edge
105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com Spur Gear Terms and Concepts Description In order to design, build and discuss gear drive systems it is necessary
More informationPERT Computerized Placement Test
PERT Computerized Placement Test REVIEW BOOKLET FOR MATHEMATICS Valencia College Orlando, Florida Prepared by Valencia College Math Department Revised April 0 of 0 // : AM Contents of this PERT Review
More information6 EXTENDING ALGEBRA. 6.0 Introduction. 6.1 The cubic equation. Objectives
6 EXTENDING ALGEBRA Chapter 6 Extending Algebra Objectives After studying this chapter you should understand techniques whereby equations of cubic degree and higher can be solved; be able to factorise
More information1. What data might a car leave behind at the scene of an accident?
Bellwork 21015 It takes 8,460 bolts to assemble an automobile, and one nut to scatter it all over the road. Author Unknown 1. What data might a car leave behind at the scene of an accident? 1 5 9 ACCIDENT
More informationGRADE 7. Mathematics. Administered April 2013 RELEASED
GRADE 7 Mathematics Administered April 03 RELEASED Copyright 03, Texas Education Agency. All rights reserved. Reproduction of all or portions of this work is prohibited without express written permission
More informationCustomary Length, Weight, and Capacity
15 CHAPTER Lesson 15.1 Customary Length, Weight, and Capacity Measuring Length Measure each object to the nearest inch. 1. The crayon is about inches long. 2. 3. The toothbrush is about The rope is about
More informationVirginia Placement Test Practice Questions and Answers
Virginia Placement Test Practice Questions and Answers Table of Contents Practice Problems for MTE Operations with Positive Fractions... Practice Problems for MTE Operations with Positive Decimals and
More informationVoltage Loss Formula s
www.litzwire.com HM Wire International Inc. Phone: 3302448501 Fax: 3302448561 Voltage Loss Formula s www.hmwire.com Voltage loss in a wire is synonymous to pressure loss in a pipe. Electric current
More informationQuadratic Equations and Functions
Quadratic Equations and Functions. Square Root Propert and Completing the Square. Quadratic Formula. Equations in Quadratic Form. Graphs of Quadratic Functions. Verte of a Parabola and Applications In
More informationSuch As Statements, Kindergarten Grade 8
Such As Statements, Kindergarten Grade 8 This document contains the such as statements that were included in the review committees final recommendations for revisions to the mathematics Texas Essential
More informationMATH 100 PRACTICE FINAL EXAM
MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number
More informationDear Accelerated PreCalculus Student:
Dear Accelerated PreCalculus Student: I am very excited that you have decided to take this course in the upcoming school year! This is a fastpaced, collegepreparatory mathematics course that will also
More informationMathematics Placement Examination (MPE)
Practice Problems for Mathematics Placement Eamination (MPE) Revised August, 04 When you come to New Meico State University, you may be asked to take the Mathematics Placement Eamination (MPE) Your inital
More information7 Scale Model of the Solar System
Name: Date: 7 Scale Model of the Solar System 7.1 Introduction The Solar System is large, at least when compared to distances we are familiar with on a daytoday basis. Consider that for those of you
More informationKeystone National Middle School Math Level 8 Placement Exam
Keystone National Middle School Math Level 8 Placement Exam 1) A cookie recipe calls for the following ingredients: 2) In the quadrilateral below, find the measurement in degrees for x? 1 ¼ cups flour
More informationSQUARESQUARE ROOT AND CUBECUBE ROOT
UNIT 3 SQUAREQUARE AND CUBEUBE (A) Main Concepts and Results A natural number is called a perfect square if it is the square of some natural number. i.e., if m = n 2, then m is a perfect square where m
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More informationInterpreting Graphs. Interpreting a Bar Graph
1.1 Interpreting Graphs Before You compared quantities. Now You ll use graphs to analyze data. Why? So you can make conclusions about data, as in Example 1. KEY VOCABULARY bar graph, p. 3 data, p. 3 frequency
More informationConversions between the common units of length used in the Imperial system are listed below 12 in = 1 ft 3 ft = 1 yard 1760 yards = 1 mile
THE METRIC SYSTEM The metric system or SI (International System) is the most common system of measurements in the world, and the easiest to use. The base units for the metric system are the units of: length,
More informationSection 2.3 Solving Right Triangle Trigonometry
Section.3 Solving Rigt Triangle Trigonometry Eample In te rigt triangle ABC, A = 40 and c = 1 cm. Find a, b, and B. sin 40 a a c 1 a 1sin 40 7.7cm cos 40 b c b 1 b 1cos40 9.cm A 40 1 b C B a B = 90  A
More information2Digital tablets or computer scanners can
Appendix A Measuring Lake Surface Area Lake surface area can be measured with a bathymetric map using any of the following techniques: 1One of the most accurate methods is to use a planimeter to trace
More information( ) where W is work, f(x) is force as a function of distance, and x is distance.
Work by Integration 1. Finding the work required to stretch a spring 2. Finding the work required to wind a wire around a drum 3. Finding the work required to pump liquid from a tank 4. Finding the work
More informationSimplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
MAC 1105 Final Review Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 1) 8x 249x + 6 x  6 A) 1, x 6 B) 8x  1, x 6 x 
More information9Objective 1: The student will describe functional relationships in a variety of ways.
Texas Assessment of Knowledge and Skills Grade: 09 Subject: Mathematics Administration: Spring 2003 NOTE: Measurement questions may have had scale altered in duplication. 9Objective 1: The student will
More informationNASA Explorer Schools PreAlgebra Unit Lesson 2 Teacher Guide. Solar System Math. Comparing Mass, Gravity, Composition, & Density
National Aeronautics and Space Administration NASA Explorer Schools PreAlgebra Unit Lesson 2 Teacher Guide Solar System Math Comparing Mass, Gravity, Composition, & Density http://quest.nasa.gov/vft/#wtd
More informationModel the Sun and Earth
Model the Sun and Earth How big is the Sun compared with Earth? Description Make scale models of the Sun and Earth out of paper mache. Age Level: 10 and up Materials one yellow balloon ruler thread of
More informationFind the length of the arc on a circle of radius r intercepted by a central angle θ. Round to two decimal places.
SECTION.1 Simplify. 1. 7π π. 5π 6 + π Find the measure of the angle in degrees between the hour hand and the minute hand of a clock at the time shown. Measure the angle in the clockwise direction.. 1:0.
More informationRETURN TO THE MOON. Lesson Plan
RETURN TO THE MOON Lesson Plan INSTRUCTIONS FOR TEACHERS Grade Level: 912 Curriculum Links: Earth and Space (SNC 1D: D2.1, D2.2, D2.3, D2.4) Group Size: Groups of 24 students Preparation time: 1 hour
More informationPrentice Hall Connected Mathematics 2, 7th Grade Units 2009
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems
More information83 Dot Products and Vector Projections
83 Dot Products and Vector Projections Find the dot product of u and v Then determine if u and v are orthogonal 1u =, u and v are not orthogonal 2u = 3u =, u and v are not orthogonal 6u = 11i + 7j; v
More information1. Title: Relative Sizes and Distance in the Solar System: Introducing Powers of Ten
1. Title: Relative Sizes and Distance in the Solar System: Introducing Powers of Ten Here we're going to learn how big the Sun is relative to the different types of planet in our Solar System and the huge
More informationUnderstanding Advanced Factoring. Factor Theorem For polynomial P(x), (x  a) is a factor of P(x) if and only if P(a) = 0.
61 LESSON Understanding Advanced Factoring Warm Up New Concepts 1. Vocabulary A polynomial of degree one with two terms is a.. True or False: The GCF of x 4 y 5  xy + is xy. (11) (). Divide 4x  x +
More informationExplore architectural design and act as architects to create a floor plan of a redesigned classroom.
ARCHITECTURAL DESIGN AT A GLANCE Explore architectural design and act as architects to create a floor plan of a redesigned classroom. OBJECTIVES: Students will: Use prior knowledge to discuss functions
More informationENGLISH CONTENT. Instructions for Using Your Computer Watch
ENGLISH CONTENT Instructions for Using Your Computer Watch Two Rotation System of Scale Ring Rotate System Crown Rotate System Ring Rotate System Crown Rotate System Figure 1 Instructions for Using your
More informationFORM 3 MATHEMATICS SCHEME C TIME: 30 minutes Non Calculator Paper INSTRUCTIONS TO CANDIDATES
DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department for Curriculum Management and elearning Educational Assessment Unit Annual Examinations for Secondary Schools 2011 C FORM 3 MATHEMATICS SCHEME
More informationVoyager Sopris Learning Vmath, Levels CI, correlated to the South Carolina College and CareerReady Standards for Mathematics, Grades 28
Page 1 of 35 VMath, Level C Grade 2 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 3: Lesson 4: 156159 Module 4: Lesson 7: 220223 2. Reason both contextually
More informationAssume you have 40 acres of forestland that was
A l a b a m a A & M a n d A u b u r n U n i v e r s i t i e s ANR1371 Basal Area: A Measure Made for Management Assume you have 40 acres of forestland that was recently assessed by a natural resource
More informationSECTION 16 Quadratic Equations and Applications
58 Equations and Inequalities Supply the reasons in the proofs for the theorems stated in Problems 65 and 66. 65. Theorem: The complex numbers are commutative under addition. Proof: Let a bi and c di be
More informationLecture Presentation Chapter 7 Rotational Motion
Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class
More informationTennessee Mathematics Standards 20092010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes
Tennessee Mathematics Standards 20092010 Implementation Grade Six Mathematics Standard 1 Mathematical Processes GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical
More information